-wave superconducting ground states away from half-filling are obtained from the higher-spin states at half-filling through SO(5) rotations. The SO(5) symmetry is found to be robust against the inclusion of longer-ranged Coulomb repulsion and next-nearest-neighbor hopping.

DOI: 10.1103/physrevb.57.13781

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From Antiferromagnetism to Superconductivity: Numerical Evidence for SO(5) Symmetry

R. Eder, Werner R. Hanke, S. C. Zhang

In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization, we verify the recently proposed SO(5) multiplet structures for a widely used microscopic model, the t-J model. Our results show that the d-wave superconducting ground states away from half-filling are obtained from the higher spin states at half-filling through SO(5) rotations, that the dominant low energy resonance in the dynamical spin correlation function corresponds to a `pi-resonance' in the entire low doping region, and that the SO(5) symmetry is robust against inclusion of longer ranged Coulomb repulsion and next-nearest neighbor hopping.In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization, we verify the recently proposed SO(5) multiplet structures for a widely used microscopic model, the t-J model. Our results show that the d-wave superconducting ground states away from half-filling are obtained from the higher spin states at half-filling through SO(5) rotations, that the dominant low energy resonance in the dynamical spin correlation function corresponds to a `pi-resonance' in the entire low doping region, and that the SO(5) symmetry is robust against inclusion of longer ranged Coulomb repulsion and next-nearest neighbor hopping.

arXiv:cond-mat/9707233Jul 22, 19970 citations

Fidelity study of the superconducting phase diagram in the two-dimensional single-band Hubbard model

Chunjing Jia, Brian Moritz, Cheng-Chien Chen +2 more

Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range $d$ -wave pair field term, which precipitates a superconducting state in the $d$ -wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the $d$ -wave pair/spin/charge-density matrices. The calculations show a $d$ -wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion $U$ and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. We also demonstrate that negative ${t}^{\ensuremath{'}}$ plays an important role in facilitating $d$ -wave superconductivity.Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range $d$-wave pair field term, which precipitates a superconducting state in the $d$-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the $d$-wave pair/spin/charge-density matrices. The calculations show a $d$-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion $U$ and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. We also demonstrate that negative ${t}^{\ensuremath{'}}$ plays an important role in facilitating $d$-wave superconductivity.

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Dynamics of an SO(5)-symmetric ladder model

R. Eder, Ansgar Dorneich, M. G. Zacher +2 more

We discuss properties of a recently proposed exactly SO(5)-symmetric ladder model. In the strong coupling limit we demonstrate how the SO(3)-symmetric description of spin ladders in terms of bond bosons can be upgraded to an SO(5)-symmetric bond-boson model, which provides a particularly simple example for the concept of SO(5) symmetry. Based on this representation we show that antiferromagnetism and superconductivity can be understood as condensation of either magnetic or charged bosons into a resonating-valence-bond vacuum. We identify exact eigenstates of a finite cluster with general multiplets of the SO(5) group, and present numerical results for the single particle, spin and charge spectra of the SO(5)-symmetric model and identify ``fingerprints'' of SO(5) symmetry in these. In particular we show that SO(5) symmetry implies a ``generalized rigid band behavior'' of the photoemission spectrum, i.e., spectra for the doped case are rigorously identical to spectra for spin-polarized states at half filling.We discuss properties of a recently proposed exactly SO(5)-symmetric ladder model. In the strong coupling limit we demonstrate how the SO(3)-symmetric description of spin ladders in terms of bond bosons can be upgraded to an SO(5)-symmetric bond-boson model, which provides a particularly simple example for the concept of SO(5) symmetry. Based on this representation we show that antiferromagnetism and superconductivity can be understood as condensation of either magnetic or charged bosons into a resonating-valence-bond vacuum. We identify exact eigenstates of a finite cluster with general multiplets of the SO(5) group, and present numerical results for the single particle, spin and charge spectra of the SO(5)-symmetric model and identify ``fingerprints'' of SO(5) symmetry in these. In particular we show that SO(5) symmetry implies a ``generalized rigid band behavior'' of the photoemission spectrum, i.e., spectra for the doped case are rigorously identical to spectra for spin-polarized states at half filling.

arXiv:cond-mat/9805120Physical review. B, Condensed matterJan 1, 199922 citations

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Stefan Meixner, Werner R. Hanke, Eugene Demler +1 more

We present numerical evidence for the approximate SO(5) symmetry of the Hubbard model on a 10-site cluster. Various dynamic correlation functions involving the $\ensuremath{\pi}$ operators, the generators of the SO(5) algebra, are studied using exact diagonalization, and are found to possess sharp collective peaks. Our numerical results also lend support to the interpretation of the recent resonant neutron scattering peaks in the YBCO superconductors in terms of the Goldstone modes of the spontaneously broken SO(5) symmetry. Perturbations such as longer-ranged hoppings and interactions do not suppress the $\ensuremath{\pi}$ resonance in interesting parameter regimes.We present numerical evidence for the approximate SO(5) symmetry of the Hubbard model on a 10-site cluster. Various dynamic correlation functions involving the $\ensuremath{\pi}$ operators, the generators of the SO(5) algebra, are studied using exact diagonalization, and are found to possess sharp collective peaks. Our numerical results also lend support to the interpretation of the recent resonant neutron scattering peaks in the YBCO superconductors in terms of the Goldstone modes of the spontaneously broken SO(5) symmetry. Perturbations such as longer-ranged hoppings and interactions do not suppress the $\ensuremath{\pi}$ resonance in interesting parameter regimes.

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U−J synergy effect for high- Tc superconductors

Liliana Arrachea, Dražen Zanchi

Using the renormalization group with included self-energy effects and exact diagonalization of small clusters we investigate the ground-state phase diagram of a two-dimensional extended Hubbard model with nearest-neighbor exchange interaction $J$ , in addition to the local Coulomb repulsion $U$ . The main instabilities are antiferromagnetism close to half filling and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the doped system. We find that self-energy effects are fatal for superconductivity in the repulsive Hubbard model (i.e., $J=0$ , $U>0$ ). The superconductivity is triggered by finite $J$ . The combined action of $J$ and $U$ interactions provide a remarkably efficient, mechanism to enhance both ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting and antiferromagnetic correlations.Using the renormalization group with included self-energy effects and exact diagonalization of small clusters we investigate the ground-state phase diagram of a two-dimensional extended Hubbard model with nearest-neighbor exchange interaction $J$, in addition to the local Coulomb repulsion $U$. The main instabilities are antiferromagnetism close to half filling and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the doped system. We find that self-energy effects are fatal for superconductivity in the repulsive Hubbard model (i.e., $J=0$, $U>0$). The superconductivity is triggered by finite $J$. The combined action of $J$ and $U$ interactions provide a remarkably efficient, mechanism to enhance both ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting and antiferromagnetic correlations.

arXiv:cond-mat/0409141Physical Review BFeb 28, 200512 citations

SU(4) Model of High-Temperature Superconductivity: Manifestation of Dynamical Symmetry in Cuprates

Yang Sun

The mechanism that leads to high‐temperature superconductivity in cuprates remains an open question despite intense study for nearly two decades. Here, we introduce an SU(4) model for cuprate systems having many similarities to dynamical symmetries known to play an important role in nuclear structure physics and in elementary particle physics. Analytical solutions in three dynamical symmetry limits of this model are found: an SO(4) limit associated with antiferromagnetic order; an SU(2) limit that may be interpreted as a d‐wave pairing condensate; and an SO(5) limit that may be interpreted as a doorway state between the antiferromagnetic order and the superconducting order. It is demonstrated that with a slightly broken SO(5) but under constraint of the parent SU(4) symmetry, the model is capable of describing the rich physics that is crucial in explaining why cuprate systems that are antiferromagnetic Mott insulators at half filling become superconductors through hole doping.The mechanism that leads to high‐temperature superconductivity in cuprates remains an open question despite intense study for nearly two decades. Here, we introduce an SU(4) model for cuprate systems having many similarities to dynamical symmetries known to play an important role in nuclear structure physics and in elementary particle physics. Analytical solutions in three dynamical symmetry limits of this model are found: an SO(4) limit associated with antiferromagnetic order; an SU(2) limit that may be interpreted as a d‐wave pairing condensate; and an SO(5) limit that may be interpreted as a doorway state between the antiferromagnetic order and the superconducting order. It is demonstrated that with a slightly broken SO(5) but under constraint of the parent SU(4) symmetry, the model is capable of describing the rich physics that is crucial in explaining why cuprate systems that are antiferromagnetic Mott insulators at half filling become superconductors through hole doping.

arXiv:cond-mat/0502074AIP conference proceedingsJan 1, 20051 citation

t\ensuremath{-}J

model, a widely used microscopic model for the high-

{T}_{c}

cuprates, form SO(5) symmetry multiplets. Our results show that the

d

d

-wave pair field term, which precipitates a superconducting state in the

d

-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the

d

-wave pair/spin/charge-density matrices. The calculations show a

d

-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion

U

and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. We also demonstrate that negative ${t}^{\ensuremath{'}}$ plays an important role in facilitating

d

-wave superconductivity.

J

, in addition to the local Coulomb repulsion

U

. The main instabilities are antiferromagnetism close to half filling and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the doped system. We find that self-energy effects are fatal for superconductivity in the repulsive Hubbard model (i.e.,

J=0

U>0

). The superconductivity is triggered by finite

J

. The combined action of

J

and

U

interactions provide a remarkably efficient, mechanism to enhance both ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting and antiferromagnetic correlations.